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Uniform Tension: the Problem and the Solution
ISSN 0236-3941. Вестник МГТУ им. Н.Э. Баумана. Сер. Машиностроение. 2017. № 5
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For comparison, the same series (7 pices) of samples were tested with the use of
the same device under the conditions uniaxial tension (UAT). In this case the grippers
of the device was attached only to two opposite sides of the cubic sample. The results
are shown in the third row of the table. Thus the comparison of test results of samples
of UTAT and UAT becomes correct, since errors of transmission of forces through
the device, stress concentration, etc. for different types of tests are almost the same.
The destruction of all samples occurred in the working area and not at the area of
attachment of the grips, which indicates their suitability.
For all the samples as in UTAT and in UAT by using the diagram of the appa-
ratus of the testing machine were recorded the diagram "force-move of grips of testing
machine". As these diagrams for all samples were linear, then the energy of rupture of
the sample can be calculated as half of the product of maximum force by the move of
the grip. The average value (7 pices) of this energy is given in the last column of the
table.
For discussion of the obtained results let us consider an isotropic material with
equal strength in all three axes
.
U
Plexiglass is such a material. The time of the de-
struction at uniaxial tension is depicted by points lying on the axes of a rectangular
coordinate system
,
U
0, 0; 0,
,
U
0; 0, 0,
.
U
The postulate of Drucker, says that the
surface of plasticity should not be sunken [1]. By analogy we can assume that the sur-
face of strength should also not be sunken. In the limiting case, this may be the plane
passing through the above point. The case of UTAT would correspond to a beam hav-
ing equal angles with all three axes. By simple geometry it can be shown that the ulti-
mate strength under UTAT
UTAT
U
is
3
= 1,73 times less than in uniaxial tension
UAT
U
/
UTAT
U
= 1,73.
Again, note that the above is the case if the surface strength flat.
The results given in table show that
UAT
U
/
UTAT
U
= 1,39
which indicates either an error of the results of the experiments or of the fact that the
surface of strength are slightly convex.
A very important result which is in need of further reflection and discussion is
that. Despite the lower strength of the samples at UTAT than UAT accumulated sam-
ple energy to the point of destruction in the first case were almost two times greater.
This indirectly suggests that in the case of UTAT energy failure criteria may be more
preferable.
The recently published article [6] provides the test results of samples [5] from
polymethyl methacrylate with sample sizes coinciding with the sizes of our articles.
The main conclusions of this article coincide with the content of our publications.
3. In a similar way, tests were carried out with two series of samples of carbon-
carbon composite material (CCCM) of the type 3D. The first series had the size